When I pick rugs with fraying fringes, or if the client raves about how brightly white were the fringes when the previous cleaner returned them- I gently pull on the fringes' end.
Winner! A gentle tug on any fringe is a must do before you work on a rug. Discuss weak fringe with the rug owner. Many rugs that have never been cleaned will have fringe that will fall off, since most rugs are treated with bleaches at the point of origin to achieve a desired patina. Very hard on the fringe.
Good thing fringe is out of style so we only see it on the traditional/floral rugs anymore.
As a general guide, if you see nicely twisted fibers like the extreme left side of the top pic, it will likely be OK. When it has lost the twist and is just individual fibers you'll be able to easily pull it off.
If you don't discuss it, and document it: Three months later, when the vacuum eats fringe that was previously held together by goo, you'll get the call that your cleaning damaged the fringe and you'll be asked to pay for refringe work.
